scholarly journals Quantum Relative Entropy of Tagging and Thermodynamics

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 138
Author(s):  
Jose Diazdelacruz
Keyword(s):  
Angular Momentum ◽  
Relative Entropy ◽  
Physical System ◽  
Total Angular Momentum ◽  
Quantum States ◽  
Restricted Class ◽  
Physical Systems ◽  
Quantum Relative Entropy ◽  
Heat Engines ◽  
Labeling System

Thermodynamics establishes a relation between the work that can be obtained in a transformation of a physical system and its relative entropy with respect to the equilibrium state. It also describes how the bits of an informational reservoir can be traded for work using Heat Engines. Therefore, an indirect relation between the relative entropy and the informational bits is implied. From a different perspective, we define procedures to store information about the state of a physical system into a sequence of tagging qubits. Our labeling operations provide reversible ways of trading the relative entropy gained from the observation of a physical system for adequately initialized qubits, which are used to hold that information. After taking into account all the qubits involved, we reproduce the relations mentioned above between relative entropies of physical systems and the bits of information reservoirs. Some of them hold only under a restricted class of coding bases. The reason for it is that quantum states do not necessarily commute. However, we prove that it is always possible to find a basis (equivalent to the total angular momentum one) for which Thermodynamics and our labeling system yield the same relation.

scholarly journals On Composite Quantum Hypothesis Testing

2021 ◽  
Author(s):  
Mario Berta ◽  
Fernando G. S. L. Brandão ◽  
Christoph Hirche
Keyword(s):  
Hypothesis Testing ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Quantum States ◽  
Quantum Hypothesis ◽  
Error Exponent ◽  
Quantum Relative Entropy ◽  
Asymmetric Quantum ◽  
Alternative Hypotheses ◽  
Quantum Hypothesis Testing

AbstractWe extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states $$\rho ^{\otimes n}$$ ρ ⊗ n against convex combinations of quantum states $$\sigma ^{\otimes n}$$ σ ⊗ n can be written as a regularized quantum relative entropy formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes an operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein’s lemma for classical probability distributions and lift the result to the non-commutative setting by using elementary properties of quantum entropy. Finally, our findings also imply an improved recoverability lower bound on the conditional quantum mutual information in terms of the regularized quantum relative entropy—featuring an explicit and universal recovery map.

scholarly journals Tensorization of the strong data processing inequality for quantum chi-square divergences

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 199
Author(s):  
Yu Cao ◽  
Jianfeng Lu
Keyword(s):  
Data Processing ◽  
Relative Entropy ◽  
Quantum Channel ◽  
Quantum States ◽  
Quantum Channels ◽  
Chi Square ◽  
Quantum Regime ◽  
Quantum Relative Entropy ◽  
Data Processing Inequality ◽  
Arbitrary Quantum

It is well-known that any quantum channel E satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum χκ2 divergences and quantum relative entropy. More specifically, the data processing inequality states that the divergence between two arbitrary quantum states ρ and σ does not increase under the action of any quantum channel E. For a fixed channel E and a state σ, the divergence between output states E(ρ) and E(σ) might be strictly smaller than the divergence between input states ρ and σ, which is characterized by the strong data processing inequality (SDPI). Among various input states ρ, the largest value of the rate of contraction is known as the SDPI constant. An important and widely studied property for classical channels is that SDPI constants tensorize. In this paper, we extend the tensorization property to the quantum regime: we establish the tensorization of SDPIs for the quantum χκ1/22 divergence for arbitrary quantum channels and also for a family of χκ2 divergences (with κ≥κ1/2) for arbitrary quantum-classical channels.

scholarly journals Total Angular Momentum Dichroism of the Terahertz Vortex Beams at the Antiferromagnetic Resonances

2021 ◽  
Vol 126 (15) ◽  
Author(s):  
A. A. Sirenko ◽  
P. Marsik ◽  
L. Bugnon ◽  
M. Soulier ◽  
C. Bernhard ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Vortex Beams

scholarly journals A Survey on Machine-Learning Based Security Design for Cyber-Physical Systems

2021 ◽  
Vol 11 (12) ◽  
pp. 5458
Author(s):  
Sangjun Kim ◽  
Kyung-Joon Park
Keyword(s):  
Machine Learning ◽  
Physical System ◽  
Large Scale ◽  
Computing System ◽  
Future Research ◽  
Physical Security ◽  
Computing Systems ◽  
Physical Systems ◽  
Security Research ◽  
Simultaneous Control

A cyber-physical system (CPS) is the integration of a physical system into the real world and control applications in a computing system, interacting through a communications network. Network technology connecting physical systems and computing systems enables the simultaneous control of many physical systems and provides intelligent applications for them. However, enhancing connectivity leads to extended attack vectors in which attackers can trespass on the network and launch cyber-physical attacks, remotely disrupting the CPS. Therefore, extensive studies into cyber-physical security are being conducted in various domains, such as physical, network, and computing systems. Moreover, large-scale and complex CPSs make it difficult to analyze and detect cyber-physical attacks, and thus, machine learning (ML) techniques have recently been adopted for cyber-physical security. In this survey, we provide an extensive review of the threats and ML-based security designs for CPSs. First, we present a CPS structure that classifies the functions of the CPS into three layers: the physical system, the network, and software applications. Then, we discuss the taxonomy of cyber-physical attacks on each layer, and in particular, we analyze attacks based on the dynamics of the physical system. We review existing studies on detecting cyber-physical attacks with various ML techniques from the perspectives of the physical system, the network, and the computing system. Furthermore, we discuss future research directions for ML-based cyber-physical security research in the context of real-time constraints, resiliency, and dataset generation to learn about the possible attacks.

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